A discontinuous reception (DRX) operation is included in the Long Term Evolution (LTE) system to achieve power saving and prolonged battery life of the user equipment. An improvement in DRX power saving usually leads to a potential increase in the packet delay. An optimum DRX configuration depends on the current traffic, which is not easy to estimate accurately, particularly for non-real-time applications. In this paper, we propose a novel way to vary the DRX cycle length, avoiding a continuous estimation of the data traffic when only non-real-time applications are running with no active real-time applications. Because a small delay in non-real- time traffic does not essentially impact the user’s experience adversely, we deliberately allow a limited amount of delay in our proposal to attain a significant improvement in power saving. Our proposal also improves the delay in service resumption after a long period of inactivity. We use a stochastic analysis assuming an M/G/1 queue to validate this improvement.
Keywords: LTE, DRX, nonreal-time traffic, power saving.
Manuscript received Oct. 3, 2015; revised Jan. 25, 2016; accepted Mar. 2, 2016.
Mohammad Tawhid Kawser (corresponding author, [email protected]), Mohammad Rakibul Islam ([email protected]), Khondoker Ziaul Islam ([email protected]), Mohammad Atiqul Islam ([email protected]), Mohammad Mehadi Hassan ([email protected]), Zobayer Ahmed ([email protected]), and Rafid Hasan (rafidhasan204@ gmail.com) are with the Department of Electrical and Electronic Engineering, Islamic University of Technology, Gazipur, Bangladesh..
I. Introduction
Long term evolution (LTE), based on the 3GPP standards, is the latest step in the evolution of cellular services. The incredibly higher data rates and better quality of services provided by LTE have motivated the advent and use of many different applications. This is causing the batteries of the user equipment (UE) to drain quickly, and battery power saving has therefore become a significant concern. The key technique to saving power and prolonging battery life is to let the UE switch off the receiver circuitry periodically. This is referred to as discontinuous reception (DRX). The periodic cycle in DRX is called the DRX cycle. The DRX cycle consists of an active period at the beginning, called the on duration, and then a period during which the receiver circuitry is off, which is called the off duration [1]. If a packet arrives during an off duration, it cannot be scheduled until the off duration is over. This enhances the packet delay, which is the main drawback of a DRX operation. A longer DRX cycle allows better power saving but with a longer packet delay. Thus, the DRX cycle length involves a trade-off between power saving and packet delay. The eNodeB configures two types of DRX cycles for use, namely, short and long DRX cycles, and as their names suggest, their lengths are short and long, respectively.
The authors of [2] through [5] investigated the impact of the DRX parameter values on the power saving and delay.
Such an investigation was also conducted for the industrial DRX model proposed by Nokia [6]. It was shown that a good amount of power saving can be achieved at the cost of delay.
Considering this fact, the authors in [7] proposed an algorithm to find feasible ranges of DRX parameter values for maximizing the power saving while satisfying a specified delay
Improvement in DRX Power Saving for Non-real-time Traffic in LTE
Mohammad Tawhid Kawser, Mohammad Rakibul Islam, Khondoker Ziaul Islam, Mohammad Atiqul Islam, Mohammad Mehadi Hassan, Zobayer Ahmed, and Rafid Hasan
constraint, as well as minimizing the delay while satisfying a specified power saving. The authors in [8] proposed a scheme to select a DRX configuration by jointly formulating the power saving and delay and considering the operator’s preference of power saving over delay. In [9], the authors proposed scaling the length of both short and long DRX cycles to choose a desired balance between power saving and delay. The authors in [10] proposed varying the duration and length of the short and long cycles; in addition, they proposed switching between short and long cycles using various patterns for the desired performance. In [11], the authors proposed an algorithm to select the appropriate DRX configuration while keeping the delay below a threshold. Although many proposals have been made to reach an appropriate DRX configuration, the current data traffic largely dictates which configuration may be appropriate, and thus the adaptation of the DRX parameters based on the current traffic can be more efficient. The authors of [3], [4], and [11] show that the continuous adaptation of DRX parameters can obtain a better performance compared to fixed DRX parameters. In [12] and [13], the authors also suggest an adaptation based on the current traffic. For an estimation of the current traffic, the authors of [12] use a single- bit feedback from the UE, which is known as a power preference indication, and has been adopted in 3GPP Release 11. The authors in [13] suggested a method for a quick estimation of the traffic using the maximum likelihood method and the properties of Gamma distribution. In [14], the authors proposed an adaptation based on the traffic where the time instants to reconfigure the DRX parameters also depend on the traffic; in addition, they showed an enhancement of power saving considering the delay constraint. The authors of [15]
proposed the use of a fuzzy logic controller to adjust the DRX cycle after the traffic is estimated.
In this paper, we propose a novel but simple way to vary the DRX cycle length, which can be applied only when non-real- time (NRT) applications are running with no active real-time (RT) applications. Examples of NRT applications include buffered streaming video, Web browsing, e-mail, chatting, FTP, and P2P file sharing,. On the other hand, examples of RT applications include voice, live streaming video, and online gaming. Unlike RT traffic, NRT traffic permits the delay requirement to slacken to a certain extent. In other words, a limited amount of delay can be allowed to NRT traffic essentially with no adverse impact on the user experience.
Therefore, we exploit the allowable delay for NRT traffic to improve the power saving in our proposal.
The processing in the access strata (AS) of the protocol stack depends on the quality-of-service (QoS) class identifier (QCI) of the data traffic. QCI takes on various attributes for different types of applications. Thus, RT and NRT traffic are treated
differently, and consequently, NRT traffic incurs a longer processing delay compared to RT traffic. This longer processing delay consumes a portion of the additional delay, which is permissible for NRT traffic in comparison with RT traffic. Nevertheless, after this consumption, it can be shown that some additional delay remains. Our proposal exploits this left over delay, and thus it deliberately increases the delay of NRT traffic within a permissible limit.
Our proposal avoids the continuous estimation of traffic. In fact, the estimation of current traffic, used in many of the proposals mentioned earlier, increases the amount of complicacy and burden. More importantly, NRT traffic is highly irregular and unpredictable. Thus, traffic estimations for NRT traffic cannot be very accurate, and an adaptation of the DRX configuration based on this estimation will not result in a very optimum outcome in practice.
In [16], the authors proposed an algorithm to adjust the DRX parameters when the delay crosses predefined high and low threshold values. The authors also proposed a second algorithm, which additionally considers the recently used modulation and coding scheme (MCS) to cross the predefined threshold values.
However, all of these threshold values need to be adaptive for an optimum performance in practice, and the proper selection or adaptation of the threshold values may not be easy. In [17], the authors proposed the UE to send an indication to the eNodeB when the application is delay tolerant. Then, the eNodeB can use the DRX MAC control element to command the UE to switch to long DRX cycles from short DRX cycles.
However, no side may be fully aware of the potential delay in packet arrival, and thus the decision for switching to a long cycle may not be optimal. Our proposal also functions for delay-tolerant applications while avoiding the overhead of the messages and admitting the uncertainty in packet arrival.
Our proposal additionally reduces the delay in service resumption when there has been a long inactivity without terminating an NRT session. Such a lengthy period of inactivity may occur for various reasons. For example, the server application may become busy and not respond for a while. In addition, the user may take a tea, coffee, or lunch break, stop to have a discussion with their co-workers, or use the restroom. In such cases, the DRX runs during this long period of inactivity.
In the existing scheme, the data transfer takes quite a while to resume after the inactivity, which can be a nuisance.
The remainder of this paper is organized as follows.
Section II shows different states associated with the DRX.
Section III describes the cause of the difference in delay between RT and NRT services, and establishes a relationship between the delays. Section IV details the proposed DRX scheme. Section V describes the development of analytical models for a performance evaluation of the proposed and
existing schemes. Section VI shows the expected performance of the proposed scheme and compares it with an existing scheme.
Finally, some concluding remarks are provided in Section VII.
II. States Associated with DRX
In an RRC_CONNECTED state, the UE initiates a DRX with short cycles, but it transitions to long cycles after a maximum number of short cycles. The eNodeB specifies the maximum number of short cycles, the lengths of the short and long cycles, and the length of an on duration. If the UE detects a packet scheduling during an on duration of the DRX cycle, it stops the DRX and begins a continuous data transfer. When the data transfer stops, the UE starts an inactivity timer. If new packets arrive, they can be scheduled while the inactivity timer is running, and thus the UE continues monitoring. If no scheduling is detected until the expiry of the timer, the UE initiates DRX cycles immediately. On the other hand, if any scheduling occurs while the inactivity timer is running, the data transfer resumes and the inactivity timer restarts after the data transfer is complete.
Thus, the inactivity timer can restart over and over again. It is uncertain how many times the inactivity timer may restart, and as such, how long it will run before being reset.
The various states associated with a DRX are shown in Fig. 1. State A indicates an ordinary data transfer, and TDAO represents its duration. State B indicates the running inactivity timer at the end of an ordinary data transfer, and TIBD represents its duration. In state B, the inactivity timer is reset before it expires because of the packet arrival. State C indicates a data transfer after state B, and TDAI represents the duration of state C. After each state C, the inactivity timer restarts. In addition, NID represents how many times the inactivity timer restarts. State D indicates the running inactivity timer when the timer can run up to its expiration time with no packet arrivals.
Here, TI represents the entire duration of the inactivity timer.
State E indicates running DRX cycles after the expiration of the inactivity timer. The short cycles will run first, and there can be N number of short cycles at maximum. After N number of short cycles, long cycles start running. Here, TS and TL
represent the length of short and long DRX cycles, respectively, and TOFF represents the duration of state E. The DRX operation is terminated if new packets arrive, and an ordinary data transfer then starts. Thus, state A appears after state E. The notations and states, shown in this section, will be used in Section V.
Fig. 1. States associated with a DRX.
AO
TD TIBD TDAI TIBD TDAI TI TOFF TDAO
A B C B C D E A
III. Difference in Delay between RT and NRT Services Each of the EPS bearers is associated with a particular QCI.
Each QCI corresponds to a priority, a packet error loss rate (PELR), and a packet delay budget (PDB). Here, the PDB indicates an upper limit for the packet delay between the UE and the policy and charging enforcement function in the core network. The delay should not exceed PDB for the case in which 98% of the packets have not been dropped owing to congestion. The QoS requirements are quite different between the RT and NRT traffic, and thus they assume a different QCI.
RT traffic has a stringent delay requirement, whereas some level of packet loss can be acceptable. Conversely, NRT traffic is error-sensitive, but the transmission delay can be larger. The PELR is typically 103 and 106 for RT and NRT traffic, respectively. In addition, the PDB is typically 100 and 300 ms for RT and NRT traffic, respectively [18]. The processing in AS depends on the QCI of the EPS bearer, and consequently, RT and NRT services differ in their processing delays. The scheduling of radio resources at the MAC layer uses algorithms, which treat RT and NRT traffic differently [19].
Similarly, the RLC layer uses different modes for RT and NRT traffic. The RT bearers typically use the unacknowledged mode (UM) of RLC because they are error-tolerant. Conversely, NRT applications typically use the acknowledged mode (AM) of RLC, which conducts retransmissions to limit the number of errors.
The major factor that can be attributed to the difference in the processing delay between RT and NRT traffic is the use of RLC modes. This is because the retransmissions in RLC AM incur a certain amount of delay. The RLC can receive out-of- sequence PDUs. If the receiving RLC entity finds a gap in the sequence of the PDUs, it starts a reordering timer. When the timer expires without the arrival of the missing PDU, the receiving entity infers that the PDU has been lost. At this juncture, RLC UM does not attempt to recover the lost PDUs, but RLC AM does. The receiving RLC AM entity sends a status report that includes a positive acknowledgement for the correctly received PDUs and negative acknowledgement for the fully and partially missing PDUs. The transmitting RLC AM entity then retransmits the missing data [1]. The overall delay during the correction of the data can be estimated as a summation of the reordering timer value and the round trip time (RTT). The RTT includes the round trip propagation delay and processing delay at both ends. The reordering timer value is configured by the eNodeB.
Let us assume that E[DRT] and E[DNRT] represent the expected delay for RT and NRT traffic, respectively. Here, E[DRTX] represents the expected delay for RLC AM retransmissions, which occurs only in the case of NRT traffic.
Ignoring all minor causes of differences in the delays between RT and NRT traffic, we relate these delays in crude terms as
NRT
RT
RTX
.E D E D E D (1) The PDB for NRT traffic is much larger than that of RT traffic because of the delay tolerance of NRT applications.
Thus, PDBNRT – PDBRT > E[DNRT] – E[DRT], where PDBNRT
and PDBRT denote the PDB for NRT and RT traffic, respectively. Thus, we obtain
NRT RT NRT RT ,
PDB PDB E D E D (2) where can be expressed using (1) as
NRT RT RTX .
PDB PDB E D
(3)
IV. Proposed DRX Scheme
We propose a novel way to vary the DRX cycle length such that it improves the power saving while increasing the delay of NRT traffic within a permissible limit. The proposed scheme is based on the fact that PDBNRT – PDBRT = E[DNRT] – E[DRT] can be permissible in the system. Therefore, according to (2), E[DNRT] can be allowed to be increased to a new value E[DNRT]new given by
NRT
new
NRT
NRT,E D E D (4) where
NRT .
(5) Here, (5) sets a constraint. In our proposal, E[DNRT] is increased purposely to achieve an improvement in power saving while satisfying the constraint in (5). To accomplish this through a simple method, we propose that the DRX cycle length start increasing linearly with time. A simple method can invoke small changes in the associated protocols and help achieve an easy and quick implementation. In our proposal, instead of allowing a few short cycles at the beginning, the DRX cycle length continues increasing from TS using a fixed step size Tst
until it reaches TL. Let us assume that n number of cycles are taken to reach TL. Once n DRX cycles have been executed with no packet arrivals, we consider that there has already been a long inactivity in the session. Our proposal attempts to limit delay in service resumption after a long period of inactivity.
Because a smaller DRX cycle length reduces this delay, we propose that after n DRX cycles, the DRX cycle length start decreasing from TL to TS by the same fixed step size Tst. After completion of this decline up to TS, assuming that the service may not resume soon, an increase in the DRX cycle length with the previous pattern is applied. This increase will be followed by a decrease for the same reason as before. These
Fig. 2. Existing and proposed schemes for DRX cycles.
DRX cycle length
TL
TS N short cycle
(existing)
TT Time
Tst
n DRX cycle (proposed)
Existing scheme Proposed scheme
alternate repetitions continue to lead to a triangular variation in the DRX cycle length, as illustrated in Fig. 2. The smooth gradual variation in the DRX cycle length can be expected to match a change in the data traffic to a certain extent, and thus an estimation of the data traffic is avoided. We propose that the eNodeB configure TS, TL, and Tst using a layer 3 message when a session is set up, and for this configuration, the eNodeB considers the operator’s choice and an overall estimate of the potential traffic. The period of triangular variation is TT = 2nTS
+ n(n + 1)Tst. The numerical examples in Section VI indicate that the proposed scheme can satisfy the constraint in (5).
We also propose a new factor for estimating the power saving in a DRX analysis. Various factors have been previously used. In [20], the authors apply the percentage of power saving as
Data OFF OFF
Total Data Total
100,
E T P E T
E T P E T
where the power consumption during a data transfer and during the period of DRX cycles is denoted as PData and POFF, respectively. The expected durations of these two states are denoted as E[TData] and E[TOFF], respectively. Here, E[TTotal] represents the entire mean duration including a data transfer and DRX. The authors in [4] apply the power saving factor as
S ON L ON
Total
E T T E T T , E T
where E[TS – TON] and E[TL – TON] represent the expected short and long DRX periods, respectively, excluding the on durations. In [21] and [22], the authors apply the power saving factor as E[TOFF]/E[TTotal] without incorporating any power levels. However, there is a significant difference in the power consumption during an effective data transfer, during the period in which the inactivity timer runs while looking for data, and during a DRX. Thus, we suggest an incorporation of the power levels in a power saving estimation, while introducing a third power level, Pwait, which is denoted as the power consumption while the inactivity timer runs. Second, the power consumption
becomes extremely low for DRX cycles of any length [23]- [25]. In fact, the impact of the differences in power consumption for DRX cycles of different lengths and for on durations of different lengths is trivial, and thus we ignore such differences herein. We define the average power consumption as
Data Data wait wait OFF OFF
avg
Total
. . .
P E T P E T P E T ,
P E T
(6)
where E[Twait] denotes the expected duration of running the inactivity timer, and
Total
Data
wait
OFF
.E T E T E T E T (7) To better indicate the practical power saving in a DRX, we propose that the percentage of power consumption be defined as
avg Data wait wait OFF OFF
Data Total Data Total Data Total
P E T P E T P E T 100.
P E T P E T P E T
(8)
V. Analytical Model
To evaluate the proposed and existing schemes, in this section, we present analytical models using the approach presented in [21] and [26]. We assume an M/G/1 system queue.
Thus, the packet arrival follows a Poisson process and the inter- arrival times are distributed exponentially. We assume that the packet arrival rate is λ and that the service or transmission rate of the packets is μ. Thus, the mean transmission time of a packet is E[S] = 1/µ. The traffic intensity can be expressed as / . µ We assume that the system is stable with μ > λ. The probability of packet arrival in t1 duration is
1 1
0 d 1 .
t еt t еt
Thus, the probability of no packet arrival in duration t1 is 1 0t1еtdt е t1.
To estimate the power saving, we compute the percentage of power consumption using (8), and for this purpose, E[TOFF], E[Twait], and E[TData], are evaluated below for the proposed and existing schemes. Because the Poisson traffic model is short- range dependent, early events are prominent in our analysis.
1. Mean Duration of DRX Operation
The expected duration of a continuous DRX operation in the proposed scheme E[TOFF]prop can be given by
OFF
prop
R F ,E T E T E T (9) where E[TR] and E[TF] represent the mean duration of a DRX operation in the rising and falling portions of the triangular periods, respectively. The probability that no packet will arrive
in j number of triangular periods and (k 1) number of DRX cycles for the rising portion of the (j + 1) numbered triangular period, and thereafter that a packet will arrive in the next DRX cycle (that is, the kth cycle of the rising portion), can be expressed as
T
, j T .
R
j k e Rk
(10) Here, Rk is given by
, 1 (s st) ,
k R T kT
Rk e e (11) where is given by k R,
, S st S st S st
st S
( 2 ) ( 1)
( 1)
( 1) .
( )
2
k R T T T T T k T
k k T
k T
(12)
The entire duration of the DRX associated with is given Rj k, by
, T S st S st S st
st
T S
2 ( )
( 1) 2 .
( ) ( )
R
Tj k jT T T T T T kT
k k T
jT kT
(13) Here, E[TR] can be expressed as
T T
T
T T
R , ,
0 1
st
T S
1 0 0
2 T
1 1
st S
. 1
2 1 1
1 .
2
n R R
j k j k j k
n j T j T
k
k j j
T n n
T
k k
T k k
E T T
k k T
R T je kT e
e T R e R
e
k k T kT
(14) Similarly, the probability that no packets will arrive in j number of triangular periods or during the TT/2 long rising portion, as well as in (k 1) number of DRX cycles of the falling portion of the (j + 1) numbered triangular period, and that thereafter a packet will arrive in the next DRX cycle (that is, the kth cycle of the falling portion), can be expressed as
T (T/ 2)
, j T T .
F
j k e e Fk
(15) Here, Fk is given by
, [1 s ( )st ]
k F T n k T
Fk e e , (16) where k F, is given by
, s st S st
st S
( 1) ( 1)
(2 )( 1)
( 1) .
2
k F T n T T n k T
n k k T k T
(17)
The entire duration of the DRX associated with is given Fj k, by
T
, T S st S st
T
T S st
( 1) [ ( )
2
( 1) .
2 2
F ]
j k
T jT T T n T T n k T
T k k
jT kT T nk
(18)
Here, E[TF] can be expressed as
T T T
T
F , ,
0 1
( /2) T
T S st
1 0 0
3 2
T 2
1 1
T s st
.
1
2 2
1
1
1 .
2 2
T T
n F F
j k j k j k
T n j T j T
k
k j j
T
n n
T
k k
T k k
E T T
T k k
e F T je kT T nk e
e T F e F
e
T k k
kT T nk
(19) Now, E[TOFF]prop can be determined using (9), (14), and (19).
The mean duration of the DRX in the existing scheme E[TOFF]exist is given by
OFF exist S L
[ ] [ ] [ ],
E T E T E T (20) where E[TS] and E[TL] represent the mean duration of the short and long cycles, respectively. The probability that (i 1) number of short cycles will occur with no packet arrival, and that thereafter a packet will arrive during the ith short cycle, can be expressed as
s 1 s
( T) (1 T).
s i
i e e
(21) The mean number of short cycles E[NSC] is given by
s s ss
s s
SC
1 1
. (1 ) ( )
1
1 ) .
( )
(
N N
T T T
s i
i
i i
N T
N T T
E N i e e i e
e Ne
e
(22)
Here, E[TS] is given by
s
s
S S SC S s
(1 )
[ ] [ ] .
(1 )
N T N T
T
E T T E N T e Ne
e
(23)
The probability that no packet arrives in N number of short cycles or (j 1) number of long cycles, and thereafter that a packet arrives during the jthlong cycle, can be expressed as
s( L) (11 L).
N T T T
L j
j e e e
(24) Thus, the mean number of long cycles E[NLC] is given by
s L L
s L
1 LC
1 1
[ ] (1 ) ( )
1 .
N T T T
L j
j
j j
N T T
E N j e e j e
e e
(25)
In addition, E[TL] is given by
s L
L L LC L
[ ] [ ] ,
1
N T T
E T T E N T e
e
(26) and E[TOFF]exist can now be determined using (20), (23), and (26).
2. Mean Duration of Running Inactivity Timer
The probability Px that the inactivity timer will restart x times because of packet arrivals, and thereafter that the inactivity timer will expire once completing TI, can be expressed as
I I.
(1 T)x T
Px e e (27) Thus, the mean number of restarts of inactivity timer E N[ ID] is given by
I I I
D I
0
0
[ ]
1 1.
x x
T T x T
x
E N xP
e x e e
(28)As the inactivity timer runs, the occurrences in the scenario are limited to the expiration of the timer, which means that the occurrences lie only within the range as long as the timer is running. Thus, the truncated exponential distribution can be used for the packet arrivals to estimate TIBD. The truncated exponential distribution can be expressed as
I I
I
) 0
, .
( 0
1
t T
f t e t T
e
t T
(29)
In addition, E T[ IBD] can be expressed as
I I
I BD
I
0 0
I
[ ] ( )d d
1
1– .
1
T t T
T
E T tf t t te t
e T e
(30)
The mean duration of the running inactivity timer is the summation of the average period in states B and D. Because the average period in state B is E T[ IBD] [E NID] and the period in state D is TI, E[Twait] for both the existing and proposed methods can be expressed as
I
BD D
wait I I I
[ ] [ ]
1.
[ ]
T
E T E T E N T
e
(31)
3. Mean Duration of Data Transfer
The mean duration of a data transfer is the summation of the average period in states A and C. Because E N[ ID] is the
mean number of restarts of the inactivity timer, the mean duration of data transfer E[TData] for both the existing and proposed methods can be given by
AO AI D
Data D D I
[ ] [ ] [ ] [ ].
E T E T E T E N (32) When a single packet is transmitted, its mean transmission time is E[S]=1/µ. The probability of m number of packet arrivals in this 1/µ duration, Pm, is given by
/ ( / )
! ! .
µ m m
m
e e
P m m
(33)
Thus, the mean number of packet arrivals in a 1/µ duration can be shown as
0 0
! .
m m
m m
mP me m
(34) If a single packet arrives while the inactivity timer is running, within its transmission period, an additional number of packets arrive on average. These additional packets require an additional transmission period in which a further /µ/µ 2
number of packets arrive on average. This ideally increases, and the total expected transmission period is given by
2 3
AI D
0
1 1 1
[ ] .
(1 )
k k
E T
(35)
Here, E T[ DAO] can be similarly determined. During the DRX period, E[TOFF], λE[TOFF] number of packets arrive. These packets require a transmission period of E T[ OFF]/
[ OFF].
E T In this period, an additional E T[ OFF] number of packets arrive, which requires an additional transmission period of E T[ OFF] / 2E T[ OFF] . Thus, E T[ DAO] is given by
AO 2
D OFF
OFF OFF
1
[ ] [ ]{ }
[ ] [ ].
1
k k
E T E T
E T E T
(36)
Using equations (28), (32), (35), and (36), E[TData] can be expressed as
I
I
Data OFF
OFF
OFF wait
[ ] [ ] ( 1) 1
1 (1 )
[ ] 1 1
[ ] [ ] .
1
T
T
E T E T e
µ E T e
E T E T
(37)
Here, E[TData]exist and E[TData]prop can be evaluated for the existing and proposed methods, respectively, using (9), (20),
(31), and (37). Similarly, E[TTotal]exist and E[TTotal]prop can be evaluated for the existing and proposed methods, respectively, using (7).
4. Delay Performance
The delay analysis differs between cases in which the UE is running a DRX and when it is not. Let us assume that NQ
represents the number of packets in the queue, excluding those for whom the transmission is ongoing, and that WQ represents the waiting time of a packet from the moment it arrives until its transmission commences. Little’s formula then provides the following relationship:
Q Q
[ ] [ ].
E N E W (38) The mean residual service time E[R] represents the mean service or transmission time of packets currently in transmission when a packet arrives. Because E N[ Q]/ represents the service time of all packets ahead in the queue waiting for service, according to the Pollaczek Khintchine formula, the mean wait time in the queue is given by
Q Q
[ ]
[ ] [ ] E N .
E W E R
(39) Using Little’s formula, we obtain
Q Q
[ ] [ ] [ ]
[ ]. 1
E W E R E W E R
(40)
When the transmission rate is very high compared to the packet arrival rate, making μ , the packets ahead in the queue can be quickly transmitted resulting in E W[ Q]
[ ].
E R Here, E[R] has the following relationship [27]:
[ ]2
[ ] .
2 E R E S
(41) Using (40), we obtain
2 Q
[ ] [ ].
2(1 ) E W E S
(42) While the UE is not in a DRX (in states A, B, C, or D), the packet delay can be given by
2
N_DRX Q
[ ] [ ] [ ].
2(1 ) E D E W E S
(43) On the other hand, while the UE is running a DRX (in state E), the packet may arrive at any time within the DRX cycle. There will then be an additional delay E[WD] because the packets are not processed until the particular DRX cycle is over. The overall mean delay E[DDRX] can be given by
DRX Q D
[ ] [ ] [ ].
E D E W E W (44) The Poisson process has time-homogeneity. Thus, a packet can arrive at any time during the DRX cycle with equal probability, and has to wait for the rest of the DRX cycle for any process to begin. The mean wait time can be computed as one-half of the average length of the DRX cycle, and is independent of the packet arrival rate. This mean wait time is equivalent to E[R]
and E[R]prop for either the rising or falling time of the proposed method, and can be expressed as
s st s st s st
prop
s st
2
[ ] 1 ...
2 2 2
2 ( 1)
4 .
T T T T T nT
E R n
T n T
(45)
Using (40) and (45), E[WD]prop can be expressed as
s st
D prop
2 ( 1)
[ ] .
4(1 )
T n T
E W
(46) The mean delay in the case of rising time E[DDRX]R and falling time E[DDRX]R can be expressed using (42), (44), and (46) as
DRX R DRX F Q D prop
2
s st
[ ] [ ] [ ] [ ]
2 ( 1)
[ ] .
2(1 ) 4(1 )
E D E D E W E W
T n T
E S
(47)
Denoting the probability of a packet arrival during the rising and falling times of the proposed method as and R , F respectively, they can be expressed as
R R
Total prop
[ ]
[ ]
E T
E T (48) and
F F
Total prop
[ ] [ ] .
E T
E T (49) Thus, the overall packet delay for the proposed method E[DNRT]prop can be expressed as
NRT prop R F N_DRX R DRX R F DRX F
2 st
R F s
[ ] (1 ) [ ] [ ] [ ]
1 [ (
] ( 1)
2(1 ) ) 2 .
E D E D E D E D
n T
E S T
(50) Similarly, E[WD] can be estimated for the existing method as E[WD]exist_s and E[WD]exist_L for short and long DRX cycles, respectively, and can be expressed as
s D exist_S
[ ]
2(1 ) E W T
(51) and
L exist_L
[ ] .
2(1 )
D
E W T
(52)
Denoting the probability of a packet arrival during a short cycle and a long cycle of the existing method as and s
L,
respectively, they can be expressed as
s s
Total exist
[ ] ] [ E T
E T (53) and
L L
Total exist
[ ] .
[ ]
E T
E T (54) The overall packet delay for the existing method E[DNRT]exist can be expressed as
s
NRT exist s L Q s Q
L
L Q
2
S S L L
[ ] 1 [ ] [ ]
2(1 ) [ ]
2(1 )
1 [ ] .
2(1 )
E D E W E W T
E W T
E S T T
(55)
The mean delay in service resumption after a long inactivity, without terminating the session, can be estimated as E[WD].
Thus, it will be E[WD]prop and E[WD]exist_L for the proposed and existing methods, given by (46) and (52), respectively. When μ λ, E W[ D prop] E R[ ]prop, and E W
D exist_L TL, E[WD] will not vary significantly with the packet arrival rate.VI. Numerical Results
The performance was evaluated for the proposed and existing methods numerically using the analytical models. In [18], typical PDB values of PDBRT = 100 ms and PDBNRT = 300 ms are given. As shown in Section III, the overall delay owing to RLC retransmissions can be estimated as a summation of the reordering timer value and RTT. The RTT is commonly estimated as 8 ms [1]. The reordering timer value can take values between zero and 100 ms with 5 ms gaps, or values between 100 and 200 ms with 10 ms gaps [28].
Assuming that all reordering timer values in the specifications are likely to occur equally, we set the mean reordering timer value as 85 ms. Thus, the mean overall delay owing to RLC retransmissions E[DRTX] is set to 93 ms. Using (3), can be estimated as 107 ms. Thus, the constraint in (5) is ΔNRT ≤ 107 ms. A performance evaluation was conducted for three different cases, the assumptions of which are shown in Table 1.
Here, μ λ is typically used. The values of TI, TS, andTL in Table 1 comply with the permissible values in [28]. The values of PData, Pwait, and POFF in Table 1 follow the UE power consumption model used in [23] through [25].
Table 1. Simulation assumptions.
Parameter Case 1 Case 2 Case 3
TS 20 ms 10 ms 10 ms
TL 320 ms 640 ms 40 ms
Tst 20 ms 30 ms 10 ms
n 15 21 3
TI 10 ms
N 1, 2, 3, 4, 5, 8, 12 and 16
PData 500 mW
Pwait 255 mW
POFF 11 mW
Packet arrival rate (λ) 0.05 to 0.5 packets/ms Service rate (μ) 100 packets/ms
Figure 3 shows that, in case 1, the percentage of power consumption has significantly improved in the proposed method compared to the existing method for almost all packet arrival rates λ. Figure 4 shows the relative DRX period E[TOFF]/E[TTotal], which indicates that the proposed method exhibits a much longer DRX period in most cases. However, the existing method with N = 1 has a better power saving for a significant range of λ. The power saving is also slightly better for N = 2 but for a very limited range of λ. Evidently, as the packet arrival rate increases, the duration for a data transfer and inactivity timer increases while terminating the DRX operation quicker, and consequently, the power saving declines in all cases. The authors in [8] showed that short DRX cycles are very effective in reducing the latency. This is also demonstrated in Fig. 5, in which the delay takes the best values for the existing method with a very large number of short DRX cycles.
We use this delay performance as the benchmark to evaluate ΔNRT for other cases. Compared to this benchmark, the proposed method has a roughly 60 ms longer delay for λ = 0.05 packets/ms, and thus we assume ΔNRT = 60 ms. This increase in delay can be tolerable because ΔNRT ≤ 107 ms. Conversely, the existing method with N = 1 has almost a 120-ms longer delay for λ = 0.05 packets/ms, and this increased delay may not be acceptable because ΔNRT > 107 ms. Thus, repudiating the existing method with N = 1, the proposed method still shows the best performance. The delay is found to drop almost linearly with the packet arrival rate for the proposed case, which is partly due to the fact that the DRX cycle length decreases linearly in the reverse time scale, and a higher packet arrival rate increases the likelihood of terminating a DRX operation during an earlier DRX cycle.
Figure 6 shows that, in case 2, the percentage of power
Fig. 3.Percentage of power consumption vs. packet arrival rate (case 1).
0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 10
20 30 40 50
0.50 Packet arrival rate (packets/ms)
Percentage power consumption (%)
N = 1 N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case 5
15 25 35 45
Fig. 4. Relative DRX period (E[TOFF]/E[TTotal])vs. packet arrival rate (case 1).
0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.2
0.4 0.6 0.8 1.0
0.50 Packet arrival rate (packets/ms)
Relative DRX period
N =1 N =2 N =3 N =4 N =5 N =8 N =12 N =16 Proposed case
0.1 0.3 0.5 0.7 0.9
Fig. 5. Overall packet delay vs. packet arrival rate (case 1).
0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 20
40 60 80 100 120 140
0.50 N = 1
N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case
Packet arrival rate (packets/ms)
Overall packet delay (ms)
consumption improves greatly in the proposed method for a significant range of λ, except when the existing method has N = 1, 2, or 3. The power saving is slightly better in the existing
Fig. 6. Percentage power consumption vs. packet arrival rate (case 2).
0.05 0 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 10
20 30 40 50
0.50 Packet arrival rate (packets/ms)
Percentage power consumption (%)
N = 1 N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case 5
15 25 35 45
Fig. 7. Overall packet delay vs. packet arrival rate (case 2).
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0
50 100 150 200 250 300 350
0.50 N = 1
N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case
Packet arrival rate (packets/ms)
Overall packet delay (ms)
methods with N = 4 or 5, but for a very limited range of λ. As shown in Fig. 7, compared to the benchmark, the proposed method has an increase in delay of ΔNRT = 100 ms for λ = 0.05 packets/ms. This increased delay can be tolerable because ΔNRT ≤ 107 ms. Conversely, the delay in the existing method, even with N = 4, is almost 200 ms longer than the benchmark for λ = 0.05 packets/ms. Thus, the existing method is unacceptable for small values of N as ΔNRT > 107 ms. Consequently, the proposed method can be regarded as the best option.
In case 3, a small value of TL is used. In this case, as shown in Fig. 8, the power saving improves in the proposed method compared to the existing method with any value of N. Figure 9 shows that all cases here satisfy ΔNRT ≤ 107 ms.
The mean delay in service resumption after a long period of inactivity for all three cases is shown in Table 2 for both the proposed and existing methods with λ = 0.05 packets/ms.
Because we use μ λ, this delay will not vary significantly with the packet arrival rate, and thus it is shown for a single value of λ. This delay is clearly much better in the proposed method.
In this section, the numerical examples demonstrate that a
Table 2. Mean delay in service resumption after a long period of inactivity.
Method Case 1 Case 2 Case 3
Existing method 160.08 ms 320.16 ms 20.01 ms Proposed method 90.05 ms 170.09 ms 15.01 ms
Fig. 8.Percentage of power consumption vs. packet arrival rate (case 3).
0.050 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 10
20 30 40 50
0.50 Packet arrival rate (packets/ms)
Percentage power consumption (%)
N = 1 N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case
Fig. 9. Overall packet delay vs. packet arrival rate (case 3).
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0
2 4 6 8 10 12 14
0.50 N = 1
N = 2 N = 3 N = 4 N = 5 N = 8 N = 12 N = 16 Proposed case
Packet arrival rate (packets/ms)
Overall packet delay (ms)
significantly better power saving is achieved in the proposed method with a permissible increase in packet delay. The existing method may frequently attain an even better power saving with very small values of N, but its associated delay might exceed the tolerable limit. The delay in service resumption after a long period of inactivity is consistently better in the proposed method.
VII. Conclusion
In this paper, we presented a tradeoff between power saving
